Place the ground beef in a large pot and throw in the garlic. Cook over medium heat until browned. Drain off the excess fat, and then pour in the tomato sauce, chili powder, cumin, oregano, salt and cayenne. Stir together well, cover, and then reduce the heat to low. Simmer for 1 hour, stirring occasionally. If the mixture becomes overly dry, add 1/2 cup water at a time as needed.
After an hour, place the masa harina in a small bowl. Add 1/2 cup water and stir together with a fork. Dump the masa mixture into the chili. Stir together well, and then taste and adjust the seasonings. Add more masa paste and/or water to get the chili to your preferred consistency, or to add more corn flavor. Add the beans and simmer for 10 minutes. Serve with shredded Cheddar, chopped onions, tortilla chips and lime wedges.